论文标题
复杂的对称toeplitz运算符的表征
Characterizations of complex symmetric Toeplitz operators
论文作者
论文摘要
我们介绍了复杂对称的Toeplitz运算符的完整特征。这是希尔伯特空间上共轭特征的副产品。值得注意的是，我们证明每一个共轭都承认了规范的分解。结果，我们证明，只有当Toeplitz操作员为单方面换档$ S $的toeplitz运算符和Toeplitz operrix toeplitz operrix的转换等于与Toeplitz Operrix相当于toeplitz Operator of toeplitz Operator ships $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ S $。另外，我们表征了开放单元polydisc上强壮空间上复杂的对称托管操作员。我们的结果回答了有关复杂对称托管操作员的特征的众所周知的开放问题。
We present complete characterizations of Toeplitz operators that are complex symmetric. This follows as a by-product of characterizations of conjugations on Hilbert spaces. Notably, we prove that every conjugation admits a canonical factorization. As a consequence, we prove that a Toeplitz operator is complex symmetric if and only if the Toeplitz operator is $S$-Toeplitz for some unilateral shift $S$ and the transpose of the Toeplitz operator matrix is equal to the matrix of the Toeplitz operator corresponding to the basis of the unilateral shift $S$. Also, we characterize complex symmetric Toeplitz operators on the Hardy space over the open unit polydisc. Our results answer the well known open question about characterizations of complex symmetric Toeplitz operators.
